Christian argued that everything must have a creator

[TheRealJoeFish]

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We agree that chemical processes exist.
We agree that no one has observed this specific chemical process happening naturally.
We postulate that since scientists can arrange for a specific naturalistic process to take place, it might have taken place in the past without arrangement (or naturally).
How can we prove that if something could have happened it did happen?

Given that it has not been observed, we cannot answer the question scientifically.  It is an issue of probability.  The mathematical calculations surrounding the probability of these processes occurring naturally when compared to the law of probability show that it would never happen.

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Walter Bradley, PhD, materials science, and Charles Thaxton, PhD, chemistry,5 calculated that the probability of amino acids forming into a protein is: 4.9 x 10-191 (Thaxton, Bradley, and Olsen, The Mystery of Life’s Origin, p. 80.)  

"No matter how large the environment one considers, life cannot have had a random beginning . . . there are about two thousand enzymes, and the chance of obtaining them all in a random trial is only one part in (10^20)^2000 = 10^-40,000, an outrageously small probability that could not be faced even if the whole universe consisted of organic soup."  Sir Fred Hoyle and Chandra Wickramasinghe, Evolution from Space (London: Dent, 1981), p. 148, 24.

According to the laws of probability, if the chance of an event occurring is smaller than 1 in 10^50, then the event will never occur (this is equal to 1 divided by 10^50 and is a very small number).( (E. Borel, Probabilities and Life, [New York: Dover Publications, 1962], p. 28.)

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That being said, there are only two (if there is a third I would like to add it to the discussion) explanations of human origins.  A designer or not a designer.  Given we have mathematically eliminated the possibility of 'no designer' we can logically infer 'a designer.'  
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This argument is flawed.  Here is why:

First, and this is a more minor issue, you've invoked a false dichotomy.  You provide the probability of chemical processes creating life (I'm going to ignore the well-known issues about the Hoyle text and very, very charitably assume its truth.  I'm also going to similarly ignore your horrible disrespectful treatment of Borel).  You then move directly into "designer" or "no designer", when you should still be on "designer" or "chemical processes" or "other non-designed, unknown mechanism".  But, as I said, that's not a big deal. (Edit: I missed that you brought this up. I do not know what a third option would be, only that you cannot definitively say it's one of those two.)

The much bigger deal is that your argument is, of course, a backwards look at probabilities; humans are very bad at doing this, and it's really easy to hide an error in logic.  So, I'm going to try to show the problem with a thought experiment description.

Let's say that you find a box.  You open it up, and it's full of 100 normal six-sided dice (you can test that they're normal by rolling them and seeing that they all come up fair).  What's more, all of them have the 6s up.  They're not all oriented the same way, and they're not all the same size or color, but the 6 sides are face up.  The probability of all the dice having the same number pointing up is (1/6)^99.  It is a far, far more reasonable supposition that someone arranged them this way than that they somehow, randomly, all ended up with 6 up.  That would be so unlikely as to boggle the mind.

However, let's say you also know that 1) no human physically, intentionally interfered with them (some machine automatically made the dice and put them in the box, and a different machine loaded the dice in a truck, and the truck hit a bump and the box fell out the back) and 2) the box rolled down a hill before it came to rest and you looked inside.  Your same logic applies: because the end result, that you have found, has a 1/(6^99) chance of happening, and you know that no human intentionally interfered with the dice, you must conclude that, because it's so unlikely the dice ended up as they did randomly, that god (or some other non-human creator) supernaturally arranged the dice as such.